In a quiz programme, the ratio of correct answers to incorrect answers is `5 : 2`. If a student gives 16 incorrect answers, then the number of correct answers given is _______ .

Options

A. 80
B. 40
C. 20
D. 30

Answer

To solve the problem, we need to find the number of correct answers given the ratio of correct answers to incorrect answers and the number of incorrect answers.

### Step-by-Step Solution:

1. **Understand the Ratio**:
The ratio of correct answers to incorrect answers is given as \(5 : 2\). This means that for every 5 correct answers, there are 2 incorrect answers.

2. **Set Up the Variables**:
Let the number of correct answers be \(C\) and the number of incorrect answers be \(I\). According to the ratio, we can express this as:
\[ \frac{C}{I} = \frac{5}{2} \]

3. **Use the Given Information**:
We are told that the student gave 16 incorrect answers. Therefore, we can substitute \(I = 16\) into the ratio:
\[ \frac{C}{16} = \frac{5}{2} \]

4. **Cross-Multiply to Solve for C**:
To find \(C\), we can cross-multiply:
\[ 2C = 5 \times 16 \]

5. **Calculate the Right Side**:
Now, calculate \(5 \times 16\):
\[ 5 \times 16 = 80 \]
So, we have:
\[ 2C = 80 \]

6. **Divide by 2 to Find C**:
Now, divide both sides by 2 to find \(C\):
\[ C = \frac{80}{2} = 40 \]

7. **Conclusion**:
The number of correct answers given by the student is \(40\).

### Final Answer:
The number of correct answers given is **40**.

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